A measure \(\mu \in \mathfrak {M}^+\)  is said to be \(c_\alpha \) -absolutely continuous if \(\mu (K)=0\)  for every compact set \(K\subset \mathbb {R}^n\)  with \(c_\alpha (K)=0\) . This certainly occurs if \(\int \kappa _\alpha \mu \,d\mu \)  is finite or, more generally, if \(\kappa _\alpha \mu \)  is locally bounded (but not conversely, see [1]}).
